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    Solareqns

    Uploaded by

    Muhammad Forhad
    The document outlines the steps to calculate general solar position as well as sunrise/sunset times. It provides formulas to calculate the fractional year, equation of time, solar declination angle, true solar time, solar hour angle, solar zenith angle, and solar azimuth. For sunrise/sunset calculations, the zenith angle is set to 90.833 degrees and the hour angle formula is adjusted to find sunrise/sunset times in minutes by factoring in longitude, equation of time, and whether it is sunrise or sunset. Solar noon is also calculated based on longitude and equation of time.

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    © All Rights Reserved
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    Solareqns

    Uploaded by

    Muhammad Forhad
    30 views2 pages
    The document outlines the steps to calculate general solar position as well as sunrise/sunset times. It provides formulas to calculate the fractional year, equation of time, solar declination angle, true solar time, solar hour angle, solar zenith angle, and solar azimuth. For sunrise/sunset calculations, the zenith angle is set to 90.833 degrees and the hour angle formula is adjusted to find sunrise/sunset times in minutes by factoring in longitude, equation of time, and whether it is sunrise or sunset. Solar noon is also calculated based on longitude and equation of time.

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    The document outlines the steps to calculate general solar position as well as sunrise/sunset times. It provides formulas to calculate the fractional year, equation of time, solar declination angle, true solar time, solar hour angle, solar zenith angle, and solar azimuth. For sunrise/sunset calculations, the zenith angle is set to 90.833 degrees and the hour angle formula is adjusted to find sunrise/sunset times in minutes by factoring in longitude, equation of time, and whether it is sunrise or sunset. Solar noon is also calculated based on longitude and equation of time.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    30 views2 pages

    Solareqns

    Uploaded by

    Muhammad Forhad
    The document outlines the steps to calculate general solar position as well as sunrise/sunset times. It provides formulas to calculate the fractional year, equation of time, solar declination angle, true solar time, solar hour angle, solar zenith angle, and solar azimuth. For sunrise/sunset calculations, the zenith angle is set to 90.833 degrees and the hour angle formula is adjusted to find sunrise/sunset times in minutes by factoring in longitude, equation of time, and whether it is sunrise or sunset. Solar noon is also calculated based on longitude and equation of time.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    General Solar Position Calculations

    NOAA Global Monitoring Division

    First, the fractional year (γ) is calculated, in radians.

    2 ℎ𝑜𝑢𝑟 − 12
    γ = ∗ (day_of_year − 1 + )
    365 24

    (For leap years, use 366 instead of 365 in the denominator.)

    From γ, we can estimate the equation of time (in minutes) and the solar declination angle (in
    radians).

    eqtime = 229.18*(0.000075 + 0.001868cos(γ) – 0.032077sin(γ) – 0.014615cos(2γ)


    – 0.040849sin(2γ) )

    decl = 0.006918 – 0.399912cos(γ) + 0.070257sin(γ) – 0.006758cos(2γ) + 0.000907sin(2γ)


    – 0.002697cos(3γ) + 0.00148sin (3γ)

    Next, the true solar time is calculated in the following two equations. First the time offset is
    found, in minutes, and then the true solar time, in minutes.

    time_offset = eqtime + 4*longitude – 60*timezone

    where eqtime is in minutes, longitude is in degrees (positive to the east of the Prime Meridian),
    timezone is in hours from UTC (U.S. Mountain Standard Time = –7 hours).

    tst = hr*60 + mn + sc/60 + time_offset

    where hr is the hour (0 - 23), mn is the minute (0 - 59), sc is the second (0 - 59).

    The solar hour angle, in degrees, is:

    ha = (tst / 4) – 180

    The solar zenith angle () can then be found from the hour angle (ha), latitude (lat) and solar
    declination (decl) using the following equation:

    cos() = sin(lat)sin(decl) + cost(lat)cos(decl)cos(ha)

    And the solar azimuth (θ, degrees clockwise from north) is found from:

    sin(𝑙𝑎𝑡) cos(𝜙) − sin(𝑑𝑒𝑐𝑙)


    cos(180 − 𝜃) = −
    cos(𝑙𝑎𝑡) sin(𝜙)
    Sunrise/Sunset Calculations

    For the special case of sunrise or sunset, the zenith is set to 90.833 (the approximate correction for
    atmospheric refraction at sunrise and sunset, and the size of the solar disk), and the hour angle
    becomes:

    cos(90.833)
    ℎ𝑎 = ±𝑎𝑟𝑐𝑐𝑜𝑠 { − tan(𝑙𝑎𝑡) tan(𝑑𝑒𝑐𝑙)}
    cos(𝑙𝑎𝑡) cos(𝑑𝑒𝑐𝑙)

    where the positive number corresponds to sunrise, negative to sunset.

    Then the UTC time of sunrise (or sunset) in minutes is:

    sunrise = 720 – 4*(longitude + ha) – eqtime

    where longitude and hour angle are in degrees and the equation of time is in minutes.

    Solar noon for a given location is found from the longitude (in degrees, positive to the east of the
    Prime Meridian) and the equation of time (in minutes):

    snoon = 720 – 4*longitude – eqtime

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